Up until now we have been discussing the strength of the various harmonic components of a tone as they are measured inside of the mouthpiece by means of a special microphone. What one hears in the concert hall is of course a very different thing. The spectrum generated inside the mouthpiece is transformed into the spectrum found in the concert hall by the selective nature of the transmission of sound from the mouthpiece out through the bell flare into the room.

Figure 16: Generalized transmission function showing the variation of acoustic energy with frequency

There are many facets to this transmission process, even without taking into account the complexities of room acoustics or the complication of our perceptual mechanism, which does a remarkable job of processing the great irregularity of room properties to give us definite impressions of the tone quality of our instruments. The qualitative nature of the transformation of the spectrum from inside the mouthpiece to that heard in the concert hall is similar to that of the treble boost control of a hi-fi amplifier. In other words, the higher components of the internally generated tone are preferentially radiated. We are only just beginning to unravel the mysteries of the transformation function.

Studies of the closely related but much simpler transformation between the internal spectrum and one obtained from a microphone located at a carefully chosen spot immediately outside the trumpet bell (as was the case in my experiments with Charles Schlueter) show that the transformation differs between loudly played and softly played notes, and that it differs from player to player much more than is the case for the internal spectrum itself. For this reason, I show only the general, qualitative nature of the transformation function in Fig. 16. It is also because of this only partially resolved complexity that I will confine my discussion of the general nature of the external spectrum to a single example, and use it as a basis for only such comments on its musical implications as are scientifically justified at the present time.

Figures 17a and 17b show the external spectra of the written C₄ (concert Bb₃) played on the modern Bb trumpet, and the concert A₃ of the Baroque D trumpet.

Figure 17a: External spectra of written C₄ (concert Bb₃) on a modern Bb trumpet

Figure 17b: External spectra of A₃ on a baroque D trumpet

These spectra are analyzed from recordings made with an external microphone, recorded on the second track of the same tape that carries the internal spectrum data from which are derived the curves shown at Fig. 13a and in Fig. 15. We can see at a glance that the external spectra produced by the two instruments are quite different. The modern trumpet has a loud-playing spectrum in which at least the second and third components are stronger than the fundamental component, whereas, in the spectrum of the Baroque instrument, all the lower partials are of more or less equal strength. During a diminuendo the spectrum, and hence the tone color, of a modern instrument changes (in the direction of simplicity) considerably more than does that of the Baroque instrument. In other words, during a decrescendo the Baroque instrument keeps its fully developed tone down to a much lower dynamic level than does a modern trumpet. The implications of this difference for the musician are considerable, especially when account is taken of a closely related acoustical distinction between the two designs. It is inherently easier on a long-bore instrument to achieve the accurately aligned resonance peaks that give stability of speech to the mid- and low-range tones of a brass instrument. For this reason a really good Baroque instrument permits comfortable playing at low dynamic levels and allows the spinning-out of diminuendos to an extent that can be quite astonishing to the player of present-day trumpets. These advantages of the design of the Baroque instrument explain why it is so difficult to maintain tonal and dynamic balance between a modern trumpet and a small chamber group of the sort called for by Bach and Handel. The player cannot 'lean into' his instrument for full tone and security of attack without drowning out everyone else. I leave a detailed discussion of these matters to other contributors to this book and will merely remark that Philip Bate's brief but well-chosen words on this subject²¹ are in entire accord with the acoustical facts described above.

Trumpet Acoustics
Acoustical Preliminaries
The "Water Trumpet"-- An Analog to What Happens inside a Trumpet
The Function of the Player's Lips
The Function of the Pipe and Bell--Inside the Air Column
The Cooperation Needed for Musical Results
The Baroque Trumpet
The 'Internal' Spectrum of the Modern Trumpet
The 'Internal' Spectrum of the Baroque Trumpet
Relation of Intrnal to External Tone Color Spectrum
The Menke Trumpet
The Problem of Clean Attack
Mahillon in Retrospect
Conclusion
Bibliographic Notes